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A certain batch of students always show up to class within 2 minutes after the the class starts, but never actually show up before class starts. Let X represent the time between the start of class and the time the students show up, with the probability density function of X as follows. Round all answers to four decimal places. R(x ) = kx 0 s xs2 otherwise a) What is the value of * that makes this a valid pdf? 2 Which of the following curves represents the density curve for the pdf above? f(x) f(x) 1.5 1.5 1.0 1.0 0.5 05 K O 0.5 1.0 1.5 2.0 X O 0.5 1.0 1.5 2.0 f(x) F(X) 1.5 1.5 1.0 1.0 05 0.5 1.0 1.5 2.0 0.5 1.0 1.5 2.0 (b) Find the probability that the batch of students show up within 1 minute of the start of class. 535 (c) Find the probability that the batch of students show up between 45 and 105 seconds after class starts. -123 (d) Find the probability that the batch of students show up at least 105 seconds after the class starts. -1